answers your sinlxyfilytxy [ ysmcxy ) - ysmlxy ) - odyz, So y '=y(encwsd. ANI : gi( encwsxtxtn 1 cos x

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1 lzn4+ 2 Zx 24 G LECTURE NOTES REVEW OF CHAPTERS 3&4 A ew wrmup derivtives Simpli our nswers Given x rcse 3x d 0 x b Fd d/dx i cosx x 2 32 e3 3 slxiltx smcx 2x xsmcx 3X 3ep_e6x smlx 2F smcx D mplicit Di odz sm4+2x smlx logrithmic o c Fd 0 i 2x+3 p di 7 d Fd g 0 x i gx cos x x 4+x 2 ln3ln2x+d m n cosx ttllu#x+xed Cosx titzxt 4252 encwsd FT 2 Ad t 2t K AN encwsxtxtn D 2 Fd eqution le tngent x +cos x cos x when x /2 pot when # E Y9" Ttl CE D E gt Y m?emjetusxxs#a*+t+pwhenxzmttztslnly2ccose%d2 2 Review Chpters 3 & 4

2 Volume h plug RZ 25 k 3 A pper cup hs shpe cone with height 0 cm nd rdius 3 cm t p wter is poured cup t rte 2 cm 3 /sec how st is wter level risg when wter is 5 cm deep? 3cm come V tz h ; O use similr trswjg # V Toh 2 F h3 n chug 2 Now tke derivtive 9 qe implicitl time t seconds with respect Ad dh 9 tch The wter is risg t rte dt % cmtseo when o z 2 wnt wter is 5cm deep h5j n 4 Fd leriztion x p x t 4nd use it estimte p 4 Know trnsltion Use tngent le cx t x4 estimte 4 Fdtngentle pot slots Estimtion "2 C x 4 tz le 2 tplzxk Ll4 D t G +2 # t4 025 didnt need clcult 4 Flt Lx will use this version 2 Review Chpters 3 & 4

3 5 Wht re criticl numbers unction? n vlues o dom tht undeed ggntuous b How do ou d blute mximum nd mimum unction on closed tervl? check Lrgest 2 vlue vlues g Mx endpots smllest criticl vlue pots m c Fd criticl numbers x s x + cos2 x 0 ] 6 cosx when Cos is 6 lws deed And 2s o criticl The re Tz s nxtz 5 lx when 2slnX0 x Cos n zwsxcs + Tht T numbers ET F 2 Stte Men Vlue Theem nd drw picture illustrte it smeslopest timidtg t#;nmeiiewhpqgmysytk C b tht b c ; b o b nor possible c b Determe wher Men Vlue Theem pplies x xx2 x 2 on ] it cn be pplied d ll numbers tht stis conclusion Men Vlue Theem??z C ed?td22g G kx l > C zc+dc 22 Onl Yz 0 Thus o is C l TL#snwsqnjcnknishrYYmmm Hett ith c " we Or need 35 d Zc c 2 tht Kd 3 e d Review Chpters 3 & 4 eodeddobgng

4 t Tb 7 Let x 2x + 2 cos x on 2 ] Fd open tervls on which unction is cresg decresg 0 Boot t sign xtengah 2 2 T x2t#2sm islwsctessmxnl Ott Note hizontl trngenb here 0 g 3 T 2 2 b Appl irst derivtive test identi ll reltive extrem Clssi ech s locl mxim locl mim Sce is lws cresg ZTD hs on locl & blute Begn tt 2 # +2 nd locl t blute Mx 2A4 # +2 c Fd open tervls on which unction is concve up concve down T " x2ws o when x o + o 0 E E 3 d Fd lection pots e Sketch grph o + nswer sign 3 " it 2 TT 3 2 T mhests m z * T cve up 2 T T T 3 } 3 on C z % nd is concve down on E u±zs3e th t tpt#i qqpt 4 Review Chpters 3 & 4

5 t 8 Evlute ollowg limits Show our wk ex x0 cos x x/x b lim lim x0 n±±xm s Let Y L n tln tr ±n E i±* xi Y tpsecureservere#thr&&2mgg 9 Fd pot on grph x x + 2 tht is closest 5 3 Be obsessive bout showg our wk cler nd gnized shion t is not suicient get crect nswer You must be ble prove tht our nswer is crect 99 GWE S±td uncti Construct nm#izoe E AlxZx 20 Derivtive Test First Appl A G wnt We 40 ALA eerie And hs mximum The Us chnge blute n t GF sign X20z cresponds locl mximum This A o exctl tervl blute be must hs no becuse criticl pot one gon P iteen on A mximum > 4g2g mximize 6 20 on C op #; right 23 F tells t cner pot 45 locl 5 Review Chpters 3 & 4